
(\(E_1\) ) An experiment with no early stopping having a fixed sample size \(n_1+n_2\)  and a joint sampling density \(\prod _{i=1}^{n_1+n_2}f_{X_i}(x_i|\theta )\) .

(\(E_2\) ) A sequential experiment with early stopping if \(\sqrt{n_1}\bar{X}_1 > 1.96\)  [motivated by an experiment with an interim test that is not adjusted for multiple testing] having joint sampling density \(\prod _{i=1}^{n_1}f_{X_i}(x_i|\theta ) \left[\prod _{i=n_1+1}^{n_1+n_2}f_{X_i}(x_i|\theta )\right]^{I\left(\sqrt{n_1}\bar{X}_1 > 1.96\right)}\) .

(\(E_3\) ) A sequential experiment with early stopping if \(\sqrt{n_1}\bar{X}_1 > 2.78\)  [motivated by the [1]} boundary] having a joint sampling density
\(\prod _{i=1}^{n_1}f_{X_i}(x_i|\theta ) \left[\prod _{i=n_1+1}^{n_1+n_2}f_{X_i}(x_i|\theta )\right]^{I\left(\sqrt{n_1}\bar{X}_1 > 2.78\right)}\) .

